Question

Cookie Monster Inc. produces cookies using two inputs, cookie dough and chocolate chips. The firm’s production function is given by Q(D,C) = D^2C, MPD = 2DC, MPC = D^2, where Q denotes the quantity of cookies per day, D the batches of cookie dough per day, and C the cups of chocolate chips per day. Assume that the price of a batch of cookie dough is $2 and the price of a cup of chocolate chips is $1.

a) How much dough and chocolate chips should the firm use to maximize pro- duction if it has a fixed budget of $900 to spend on production?
b) What is the maximum number of cookies it can produce with $900?

2. Cookie Monster Inc. produces cookies using two inputs, cookie dough and chocolate chips. The firm’s production function is given by Q(D,C)=DC, MPD =C, MPC =D, where Q denotes the quantity of cookies per day, D the batches of cookie dough per day, and C the cups of chocolate chips per day. Assume that the price of a batch of cookie dough is $1 and the price of a cup of chocolate chips is $3.
a) How much dough and chocolate chips should the firm use to produce 300 cookies at minimum cost?
b) What is the minimum cost of producing 300 cookies?

Answer 1

1.

(a) Number of dough and chocolate chips = 300

(b) Maximum number of cookies = 27000000

2.

(a) Number of dough and chocolate chips = 10

(b) Minimum cost of production = $60

Step-by-step explanation:

See the attached file for the calculation