Consider the pizza market in a small college town with the following assumptions
ID: 2778275 • Letter: C
Question
Consider the pizza market in a small college town with the following assumptions:
The market is in long-run equilibrium.
Each pizza shop sells 100 pizzas per week. (For ease of exposition, suppose that each shop sells only pizza and only one size.)
Fixed cost for each shop is $500 per week.
Price and elasticity for Salamandra's (s), Genoa's (g), Domino's (d), and Four Star (4) are:
Ps = 11.00; Es = -2.2
Pg = 11.00; Eg = 2.75
Pd = 9.00; Ed = 1.8
P4 = 8.00; E4 = -2
Based on these assumptions, answer the following questions.
A. What market structure best describes the pizza market in this town? Explain.
B. What is average variable cost at this output level for each of the four shops? Explain how you derived this result.
C. Based on your answers to questions 4a and 4b and the first through fourth assumptions from Step 3, are any of these four firms earning above-normal profit? Explain your answer.
Explanation / Answer
a) The pizza market in the town is a “Monopolistic competition”, because Monopolistic competition is a market structure where a relatively large number of sellers offering similar but not identical products. So here four different shops are selling pizzas having different prices.
b) If the Inverse Demand Function P = P(Q); i.e., P as a function of Q,
Then Total Revenue (TR) is TR = P(Q)*Q
This implies that Marginal Revenue MR (taking the derivative w.r.t. Q) is
MR = P + (dP/dQ)*Q
= P[1 + (dP/dQ)*(Q/P)]
= P[1 + (1/E)]
(where E is the Price Elasticity of Demand; i.e.,
E = (dQ/dP)*(P/Q) )
Now we know the profits are maximized where MR = MC.
Thus MC = P [1 + (1/E)]
Now based on above we can calculate the Marginal cost for each pizza shop,
Salamandra's (s) MCS = 11 x [1 + (1/-2.2)] = 6
Genoa's (g) MCg = 11 x [1 + (1/2.75)] = 15
Domino's (d), MCd = 9 x [1 + (1/1.8)] = 13.89
Four Star (4), MC4 = 8 x [1 + (1/-2)] = 4
Also we know in long run, MC = Average Total Cost.
So now total cost = average total cost x quantity produced,
Salamandra's (s) MCS = ATCS= 6
=> Total Cost (TCS) = ATCS x 100 = 6 x 100 = 600
Genoa's (g) MCg = ATCg = 15
=> Total Cost (TCg) = ATCg x 100 = 15 x 100 = 1500
Domino's (d), MCd = ATCd = 13.89
=> Total Cost (TCd) = ATCd x 100 = 13.89 x 100 = 1389
Four Star (4), MC4 = ATC4 = 4
=> Total Cost (TC4) = ATC4 x 100 = 4 x 100 = 400
As per question Fixed cost = $500
So Variable cost = Total cost – fixed cost
Also Average variable cost = (Total cost – Fixed cost ) / Quantity produced
Salamandra's (s) AVCS = (TCS – Fixed cost) / Quantity produced
=> Average Variable Cost (AVCS) = (600 – 500) / 100 =1
Genoa's (g) AVCg = (TCg – Fixed cost) / Quantity produced
=> Average Variable Cost (AVCg) = (1500 – 500) / 100 =10
Domino's (d), AVCd = (TCd – Fixed cost) / Quantity produced
=> Average Variable Cost (AVCd) = (1389 – 500) / 100 =8.89
Four Star (4), AVC4 = (TC4 – Fixed cost) / Quantity produced
=> Average Variable Cost (AVC4) = (400 – 500) / 100 =-1
c) Salamandra's (s) MCS = 6, and selling price PS= 11
Genoa's (g) MCg = 15, and selling price Pg= 11
Domino's (d), MCd = 13.89, and selling price Pd= 9
Four Star (4), MC4 = 4, and selling price P4= 8
Only for Salamandra's (s) and Four Star (4), the price is greater than Marginal cost. So these two shops are earning above normal profit.
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