suppose that Grinch and Grubb go into the wine business in a small country where wine is difficult to grow.The demand for wine is given by p  $360  .2Q, where p is the price and Q is the total quantity sold.The industry consists of just the two Cournot duopolists, Grinch and Grubb.Imports are prohibited.Grinch has constant marginal costs of $75 and Grubb has marginal costs of $15.How much Grinch's output in equilibrium?

A) 562.50
B) 187.50
C) 750
D) 375
E) 1,125

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Jasmine Aranda · Accepted Answer

Final Answer : D, Explanation :  To find the equilibrium output of each firm, we need to use the Cournot model. In this model, each firm assumes that its competitor's output will remain constant, and maximizes its own profit accordingly.Let's start with Grubb. Grubb's profit function is:πG = (p - $15)QGwhere QG is Grubb's output.To find Grubb's best output, we need to find how much wine will be sold in the market as a whole. To do that, we use the demand function:p = $360 - 0.2QSubstituting this into Grubb's profit function:πG = ($360 - 0.2Q - $15)QGSimplifying:πG = ($345 - 0.2Q)QGNow we take the derivative of this with respect to QG to find Grubb's best response function:dπG/dQG = $345 - 0.4QGSetting this equal to zero:$345 - 0.4QG = 0QG = 862.5So Grubb's best output is 862.5 units of wine.Now we can use the same method to find Grinch's best response function. Grinch's profit function is:πC = (p - $75)QCwhere QC is Grinch's output.Substituting the demand function:πC = ($360 - 0.2Q - $75)QCπC = ($285 - 0.2Q)QCTaking the derivative with respect to QC:dπC/dQC = $285 - 0.4QCSetting this equal to zero:$285 - 0.4QC = 0QC = 712.5So Grinch's best output is 712.5 units of wine.Therefore, the equilibrium output of Grinch is 375 units (since the total quantity sold in the market is 1,575), and the answer is D) 375.

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