Answer to Question #282096 in Economics for daniel

Question

1. Davit plans to consume two goods (good x and good y) with a limited budget. If Davit's budget line has intercepts 100 units of good x and 50 units of good y and price of good x (Px) is $100. Then, answer the next three questions.

A) What are Davit's income and Price of good y (Py)

B) What is the simplified version of Davit's budget line equation?

C) If Davit's utility function is given by U(X; Y) = X0.5Y 0.5, how many units of good X and good Y would he consume if he choose the bundle that maximizes his utility subject to his budget constraint?

2. Consider the following total cost function: TC = 2/3Q3 – 10Q2 + 200Q + 50

A) Identify the FC and VC function?

B) Calculate AVC, AFC, ATC, and MC functions

C) Determine the level of output at which AVC reaches minimum point and the minimum AVC at that level of output?

Answer 1

1.

A) Davit's income is: B = 100×100 = $10,000.

Price of good y (Py) is: Py = B/Y = 10,000/50 = $200.

B) The simplified version of Davit's budget line equation is:

100X + 50Y = 10,000.

C) If Davit's utility function is given by $U(X; Y) = X^{0.5} Y^{0.5}$ , then he maximizes his utility subject to his budget constraint when:

$MUx/MUy = Px/Py$

and 100X + 50Y = 10,000.

$MUx = U'(X) = 0.5(Y/X)^{0.5},$

$MUy = U'(Y) = 0.5(X/Y)^{0.5},$

Y/X = 100/50,

Y = 2X,

100X + 100X = 10,000,

X = 50 units, Y = 100 units.

2.

A) FC = 50 and $VC = 2/3Q^3 – 10Q^2 + 200Q.$

B) $AVC = VC/Q = 2/3Q^2 – 10Q + 200,$

AFC = FC/Q = 50/Q.

$ATC = AFC + AVC = 2/3Q^2 – 10Q + 200 + 50/Q,$

$MC = TC'(Q) = 2Q^2 - 20Q + 200.$

C) AVC reaches minimum point when AVC = MC.