1) Assume the market for pizza is a perfectly competitive constant cost industry and all firms have identical costs (i.e. homogenous firms). The market demand and market supply functions for this perfectly competitive industry are given below.
$$
\begin{array}{l}
P=30.5-.005 Q \
P=1.7+.003 Q
\end{array}
$$
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline $\boldsymbol{L}$ & \begin{tabular}{l}
$\boldsymbol{q}$ \
$=\boldsymbol{T} \boldsymbol{P}$
\end{tabular} & $\boldsymbol{T C}$ & $\boldsymbol{T F F}$ & $\boldsymbol{T V C}$ & $\boldsymbol{A T C}$ & $\boldsymbol{A V C}$ & $\boldsymbol{M C}$ \
\hline $\mathbf{0}$ & 0 & 100 & 100 & 0 & - & - & - \
\hline $\mathbf{1}$ & 10 & 205 & 100 & 105 & 20.50 & 10.50 & 10.50 \
\hline $\mathbf{2}$ & 20 & 245 & 100 & 145 & 12.25 & 7.25 & 4.00 \
\hline $\mathbf{3}$ & 30 & 280 & 100 & 180 & 9.33 & 6.00 & 3.50 \
\hline $\mathbf{4}$ & 40 & 340 & 100 & 240 & 8.50 & 6.00 & 6.00 \
\hline $\mathbf{5}$ & 50 & 430 & 100 & 330 & 8.60 & 6.60 & 9.00 \
\hline $\mathbf{6}$ & 60 & 545 & 100 & 445 & 9.08 & 7.42 & 11.50 \
\hline $\mathbf{7}$ & 70 & 720 & 100 & 620 & 10.29 & 8.86 & 17.50 \
\hline $\mathbf{8}$ & 80 & 930 & 100 & 830 & 11.63 & 10.38 & 21.00 \
\hline $\mathbf{9}$ & 90 & 1190 & 100 & 1090 & 13.22 & 12.11 & 26.00 \
\hline
\end{tabular}
a) Over what range of prices would the firm stay open in the short run and earn a loss?
b) Over what range of prices would the firm stay open in the short run and earn above normal profits?
c) At what price would the firm be indifferent between shutting down and staying open in the short run?
d) What price would the firm break even (earn a normal profit) in the short run?
e) Find the market equilibrium price and quantity. Show work.
f) Using marginal analysis, how does a firm find the optimal output?
g) If a firm is unable to find an output where MR=MC, then it will produce where MR still exceeds MC, but the gap is as small as possible. It's also important to note that the firm will not produce on the downward portion of its MC curve. Find the profit-maximizing output (or loss minimizing output) for an individual firm in the short-run.
h) Calculate the profits or losses for an individual firm in the short run.
i) How many firms are in the industry in the short run?
j) Show the short-run solution graphically using one graph for the market and one graph for the representative firm. Place the graphs next to one another.
k) What will happen to the price of the product in the long-run? Explain how the industry will transition from SR to LR. Comment on the following items: number of firms, supply, price, and profit.
1) Find the long-run price.
$\mathrm{m})$ How many units will an individual firm produce in the long run?
n) How many firms will exist in this industry in the long run? How many firms will enter or exit in the long run?
o) Calculate the firm's profits or losses in the long run. Prove solution.
p) Show how the market and representative firm transition from the short-run to the long-run (show this in the same graph as part $(\mathrm{k})$ ).
q) Using the graph in part (k), go back and identify the firm's short-run supply curve. You may want to use a colored pen to identify the curve. Be precise.
r) Your friend proposes that a firm would be better off if they maximized per unit profit instead of maximizing total profit. Prove to your friend that short-run total profit is lower when per unit profit is maximized. Use the following definition for per unit profit: $\frac{\pi}{q}=(P-A T C)$
s) Calculate the $\mathrm{HHI}$ in the long run for the industry. Assume all firms are identical.

Question

Accepted Answer

∻a Solution∻ ‖ a ⋮ Short-Run Shutdown Price: The firm will shut down in the short run if the price falls below the average variable cost (AVC) at the output level where marginal cost (MC) equals marginal revenue (MR), which is the price in perfect competition. ‖ ∻a Answer∻ ⚹ The firm will stay open in the short run and earn a loss if the price is above the minimum AVC but below the ATC. ⚹ ∻Key Concept∻ ⚹ Shutdown Point ⚹ ∻Explanation∻ ⚹ The shutdown point is where price equals the minimum AVC. Below this point, the firm will shut down in the short run. ⚹ ∻b Solution∻ ‖ b ⋮ Short-Run Profit: A firm earns above normal profits in the short run if the price is above the average total cost (ATC) at the output level where MC equals MR. ‖ ∻b Answer∻ ⚹ The firm will earn above normal profits if the price is above the ATC at the profit-maximizing output level. ⚹ ∻Key Concept∻ ⋮ Profit Maximization ⋮ ∻Explanation∻ ⋮ A firm maximizes profit in the short run by producing the quantity where MR equals MC, as long as the price is above ATC. ⋮ ∻c Solution∻ ‖ c ⋮ Indifference Point: The firm is indifferent between shutting down and staying open in the short run at the price equal to the minimum AVC. ‖ ∻c Answer∻ ⚹ The firm would be indifferent between shutting down and staying open in the short run at the minimum AVC, which can be found from the table provided. ⚹ ∻Key Concept∻ ⋮ Indifference Point ⋮ ∻Explanation∻ ⋮ At the minimum AVC, the firm covers its variable costs but not its fixed costs, making it indifferent to shutting down or operating at a loss. ⋮ ∻d Solution∻ ‖ d ⋮ Break-Even Price: The firm breaks even (earns a normal profit) in the short run at the price equal to the minimum ATC. ‖ ∻d Answer∻ ⚹ The firm breaks even at the price equal to the minimum ATC, which can be found from the table provided. ⚹ ∻Key Concept∻ ⋮ Break-Even Point ⋮ ∻Explanation∻ ⋮ At the break-even point, the firm covers all its costs, including a normal profit, but earns no economic profit. ⋮ ∻e Solution∻ ‖ e ⋮ Market Equilibrium: Set the market demand equation equal to the market supply equation and solve for the equilibrium price (P) and quantity (Q). ‖ ∻e Answer∻ ⚹ The market equilibrium price and quantity are found by solving the equations $P = 30.5 - 0.005Q$ and $P = 17 + 0.003Q$ simultaneously. ⚹ ∻Key Concept∻ ⋮ Market Equilibrium ⋮ ∻Explanation∻ ⋮ Market equilibrium occurs where the quantity demanded equals the quantity supplied, resulting in no tendency for the price to change. ⋮ ∻f Solution∻ ‖ f ⋮ Marginal Analysis: A firm finds the optimal output by producing up to the point where marginal revenue (MR) equals marginal cost (MC). In perfect competition, MR equals the market price. ‖ ∻f Answer∻ ⚹ The firm finds the optimal output by equating MR to MC, which is the output level where the price equals MC. ⚹ ∻Key Concept∻ ⋮ Optimal Output ⋮ ∻Explanation∻ ⋮ The optimal output maximizes profit by ensuring that the cost of producing one more unit equals the revenue it generates. ⋮ ∻g Solution∻ ‖ g ⋮ Profit-Maximizing Output: If MR=MC is not achievable, produce at the output level where MR still exceeds MC, and the gap is smallest without producing on the downward portion of the MC curve. ‖ ∻g Answer∻ ⚹ The profit-maximizing output is the highest output level before the MC curve starts to rise above the MR curve. ⚹ ∻Key Concept∻ ⋮ Profit Maximization Rule ⋮ ∻Explanation∻ ⋮ A firm maximizes profit by producing the quantity where MR exceeds MC by the smallest amount without producing where MC is falling. ⋮ ∻h Solution∻ ‖ h ⋮ Calculating Profits or Losses: Profits or losses are calculated by subtracting total costs from total revenue at the profit-maximizing output level. ‖ ∻h Answer∻ ⚹ Profits or losses for an individual firm are calculated by multiplying the difference between price and ATC by the quantity produced at the profit-maximizing output level. ⚹ ∻Key Concept∻ ⋮ Profit Calculation ⋮ ∻Explanation∻ ⋮ Profit is the difference between total revenue and total costs; if this value is negative, it represents a loss. ⋮ ∻i Solution∻ ‖ i ⋮ Number of Firms: The number of firms in the industry can be estimated by dividing the market quantity by the quantity produced by a single firm. ‖ ∻i Answer∻ ⚹ The number of firms in the industry in the short run is found by dividing the total market quantity at equilibrium by the quantity produced by one firm. ⚹ ∻Key Concept∻ ⋮ Industry Size ⋮ ∻Explanation∻ ⋮ The size of the industry in terms of the number of firms depends on the total market demand and the output of individual firms. ⋮ ∻j Solution∻ ‖ j ⋮ Graphical Solution: Draw the market demand and supply curves to find the equilibrium. Then, draw the firm's cost curves and identify the profit-maximizing output where MR=MC. ‖ ∻j Answer∻ ⚹ The short-run solution is shown graphically with the market equilibrium on one graph and the firm's profit-maximizing output on another. ⚹ ∻Key Concept∻ ⋮ Graphical Analysis ⋮ ∻Explanation∻ ⋮ Graphical analysis visually represents the equilibrium in the market and the firm's decision-making process. ⋮ ∻k Solution∻ ‖ k ⋮ Long-Run Price: In the long run, the price will adjust so that firms earn normal profits, which occurs at the price equal to the minimum ATC. ‖ ∻k Answer∻ ⚹ In the long run, the price of the product will equal the minimum ATC, where firms earn normal profits. ⚹ ∻Key Concept∻ ⋮ Long-Run Equilibrium ⋮ ∻Explanation∻ ⋮ In the long run, free entry and exit of firms ensure that the price adjusts to the point where firms earn zero economic profit. ⋮ ∻l Solution∻ ‖ l ⋮ Long-Run Output: An individual firm will produce at the output level where the price equals the minimum ATC in the long run. ‖ ∻l Answer∻ ⚹ An individual firm will produce the quantity where the price equals the minimum ATC in the long run. ⚹ ∻Key Concept∻ ⋮ Long-Run Production ⋮ ∻Explanation∻ ⋮ Firms produce at the most efficient scale, where the ATC is minimized, in the long run. ⋮ ∻m Solution∻ ‖ m ⋮ Long-Run Industry Size: The number of firms in the long run is determined by the total market demand divided by the output of an individual firm at the long-run equilibrium price. ‖ ∻m Answer∻ ⚹ The number of firms in the long run is found by dividing the total market quantity at the long-run equilibrium price by the quantity produced by one firm. ⚹ ∻Key Concept∻ ⋮ Long-Run Industry Size ⋮ ∻Explanation∻ ⋮ The long-run industry size is determined by market demand and the efficient scale of production for individual firms. ⋮ ∻n Solution∻ ‖ n ⋮ Long-Run Firm Entry/Exit: Firms will enter or exit the industry until economic profits are zero, which occurs when the price equals the minimum ATC. ‖ ∻n Answer∻ ⚹ Firms will enter or exit the industry in the long run until the number of firms adjusts so that all firms earn zero economic profit. ⚹ ∻Key Concept∻ ⋮ Long-Run Adjustments ⋮ ∻Explanation∻ ⋮ Entry and exit of firms in the long run ensure that the market reaches a point where firms earn normal profits only. ⋮ ∻o Solution∻ ‖ o ⋮ Long-Run Profits or Losses: Calculate the firm's profits or losses by comparing the price to the ATC at the long-run equilibrium output. ‖ ∻o Answer∻ ⚹ In the long run, firms earn zero economic profit, as the price will be equal to the minimum ATC. ⚹ ∻Key Concept∻ ⋮ Long-Run Profitability ⋮ ∻Explanation∻ ⋮ Economic profits are eliminated in the long run due to the entry and exit of firms, leading to a normal profit situation. ⋮ ∻p Solution∻ ‖ p ⋮ Transition Graph: Show the transition from short-run to long-run equilibrium by adjusting the supply curve to reflect entry or exit of firms until price equals the minimum ATC. ‖ ∻p Answer∻ ⚹ The transition from short-run to long-run equilibrium is shown graphically by the shift of the supply curve until the price equals the minimum ATC. ⚹ ∻Key Concept∻ ⋮ Market Transition ⋮ ∻Explanation∻ ⋮ The market transitions from short-run to long-run equilibrium as firms enter or exit, adjusting the supply until only normal profits are earned. ⋮ ∻q Solution∻ ‖ q ⋮ Short-Run Supply Curve: The firm's short-run supply curve is the portion of the MC curve above the minimum AVC. ‖ ∻q Answer∻ ⚹ The firm's short-run supply curve is identified as the portion of the MC curve that lies above the minimum AVC. ⚹ ∻Key Concept∻ ⋮ Short-Run Supply Curve ⋮ ∻Explanation∻ ⋮ The short-run supply curve for a firm in perfect competition is the MC curve above the shutdown point. ⋮ ∻r Solution∻ ‖ r ⋮ Maximizing Per Unit Profit: Show that total profit is lower when per unit profit $(P - ATC)$ is maximized instead of total profit, which is maximized where $MR = MC$. ‖ ∻r Answer∻ ⚹ Maximizing per unit profit $(P - ATC)$ leads to a lower total profit than maximizing total profit where $MR = MC$. ⚹ ∻Key Concept∻ ⋮ Profit Maximization Strategy ⋮ ∻Explanation∻ ⋮ Total profit maximization, not per unit profit maximization, should be the firm's goal, as it leads to higher overall profits. ⋮ ∻s Solution∻ ‖ s ⋮ Calculating HHI: The Herfindahl-Hirschman Index (HHI) is calculated by summing the squares of the market shares of all firms in the industry. In a perfectly competitive market with identical firms, the HHI will be low. ‖ ∻s Answer∻ ⚹ The HHI in the long run for the industry will be low, reflecting a high level of competition with many small firms. ⚹ ∻Key Concept∻ ⋮ Market Concentration ⋮ ∻Explanation∻ ⋮ The HHI measures market concentration, with lower values indicating a more competitive market structure. ⋮◊What is the profit-maximizing output level for a firm in the short run in a perfectly⍭ Generate me a similar question◊

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