Question

Suppose the short-run production function is q = 10L. If the wage rate is $40 per unit of labor,

a. AVC equals ____.b. MC equals _____.

Charlie’sdoughnut company has two separate bakeries. For bakery one, the total cost function is TCl = 100 + .005Ql2, and the marginal cost function is MC1= .01Q1. For bakery two,the total cost function is TC2 = 50 + .01Q22, and the marginal cost function is MC2= .02Q2Where Qland Q2are dozens of doughnuts.

a.How should Charlieallocate production if he wantsto produce 900 dozen doughnuts? b.What is Charlie’stotal cost of producing one dozen doughnuts in each of the two bakeries?

SHOW WORK

Answer 1

Given that short-run production function is q = 10L, we have L = 0.1q. Now the wage rate is $40 per
unit of labor, cost function is C = wL or C = 40L
C = 40*0.1q or C = 4q.
a. AVC equals VC/q = 4
b. MC equals dC/dq = 4
For bakery one, the total cost function is TCl = 100 + .005Ql2, and the marginal cost function is MC1=
.01Q1. For bakery two,the total cost function is TC2 = 50 + .01Q22, and the marginal cost function is
MC2= .02Q2
a.Charlie must allocate production using MC1 = MC2 rule if he wants to produce 900 dozen
doughnuts
Q1 + Q2 = 900 and 0.01Q1 = 0.02Q2 which giives Q1 = 2Q2
or 2Q2 + Q2 = 900
Q2 = 900/3 = 300 and Q1 = 600.
b.We have TCl = 100 + .005*(1^2) = 100.005, and TC2 = 50 + .01*(1^2) = 50.01