1. Consider a market of two small breweries located across the street from each
ID: 1142875 • Letter: 1
Question
1. Consider a market of two small breweries located across the street from each other. Market demand is P = 20 – 0.5Q where Q is the number of beer pints per day. Both firms have a marginal cost of c = 2 per pint. The beers are not differentiated and both firms can serve as many beers as much as needed. The firms compete on price.
a. What is the expected market price? What would be the associated quantity and firm profit?
b. Suppose that one brewery has a marginal cost of c1 = $2.00 but the second brewery changes its production techniques and reduces its marginal cost to c2 = $1.00. Would the market price be different from that in part a? Would firm profits be different? Explain.
c. Suppose there are three breweries on the street. One brewery has a marginal cost of c1 = $2.00 and the second and third breweries have a marginal cost of c2 = c3 = $1.00. Would the market price be different from that in part b? Would firm profits be different? Explain.
d. Going back to a market with two breweries and equal marginal costs of c = $2. If each brewery could only serve 25 pints a day, would you expect the same market price and firm profits as part a? Show any necessary work.
e. Finally, in the market with two breweries and equal marginal costs of c = $2, if consumers showed varying preferences for the beers sold by each brewery, would you expect the market price to differ from part a? Explain. (No calculations needed.)
Explanation / Answer
a. Profit maximizing condition requires MR=MC i.e marginal revenue=marginal cost
MR=d/dQ(TR)=d/dQ(PQ)=d/dQ[(10-0.1Q)Q]=10-0.2Q
Now, 10-0.2Q=2
or, Q=40
Hence, market price is $(10-0.1x40)=$6
So, profit z=PQ-CQ=$[(10-0.1x40)50-2x40]=$160
b. Both firm will individually equate their marginal cost with the marginal revenue of market demand.
Hence, for the firm 1 it is:
10-0.2Q=2
or, Q=40
Similarly for firm2 it is:
10-0.2Q=1.50
or, Q=42.5
Market price now would be $(10-0.1x40)=$6 for firm 1 and it is $(10-0.1x42.5)=$5.75 for firm 2.
Profit for firm 1 would be=$(6x40)-(2x40)=$160 and for firm 2 it is $[(5.75x42.5)-(1.5x42.5)]=$180.62
c. For firm 2 and 3 the price,produced output and profit would be same as firm it were for firm 2 in part b. In case of firm 1 it is as same as it was earning in the previous cases on the basis of same logic provided earlier.
d. If output is fixed with 30units and MC=$2 then price would be $(10-0.1x30)=$7 and profit would be $(7x30)-(2x30)=$150. Since MR=MC requires optimal output is 40units thus, with lower output than it, MR is higher than MC and thereby, profit is not maximized. Output could have been raised in this regard to maximized profit. Alternatively, to earn a profit of $160 i.e. as like initial case 30P-60=160
or, 30P=220
or, P=22/3=$7.3
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