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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.
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Answer from Sia

Posted 3 months ago

a Solution

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 Answer

The firm will earn above normal profits if the price is above the ATC at the profit-maximizing output level.

Key Concept

Explanation

c Solution

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

Explanation

d Solution

d Answer

The firm breaks even at the price equal to the minimum ATC, which can be found from the table provided.

Key Concept

Explanation

e Solution

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

Explanation

f Solution

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

Explanation

g Solution

g Answer

The profit-maximizing output is the highest output level before the MC curve starts to rise above the MR curve.

Key Concept

Explanation

h Solution

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

Explanation

i Solution

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

Explanation

j Solution

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

Explanation

k Solution

k Answer

In the long run, the price of the product will equal the minimum ATC, where firms earn normal profits.

Key Concept

Explanation

l Solution

l Answer

An individual firm will produce the quantity where the price equals the minimum ATC in the long run.

Key Concept

Explanation

m Solution

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

Explanation

n Solution

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

Explanation

o Solution

o Answer

In the long run, firms earn zero economic profit, as the price will be equal to the minimum ATC.

Key Concept

Explanation

p Solution

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

Explanation

q Solution

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

Explanation

r Solution

r Answer

Maximizing per unit profit $(P - ATC)$ leads to a lower total profit than maximizing total profit where $MR = MC$.

Key Concept

Explanation

s Solution

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

Explanation

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