Question

Assume the budget line is Y = 500 = pBB + pZZ = 5B + 10Z. Further assume that the marginal rate of substitution = MRS = -MUZ/MUB = -3B/Z.

With burritos (B) on the vertical axis and pizza (Z) on the horizontal axis, the marginal rate of transformation, MRT, is equal to

In equilibrium, where MRT = MRS, what is the ratio of burrito consumption to pizza consumption?

Assuming the entire budget is spent on pizza and burritos, how many pizzas are consumed?

In the short run a firm cannot vary its capital, which is fixed at K = 2, but it can vary its labor L. There are two production functions (a) q = 5L + K and (b) q = L0.5K0.5. Which of these two production functions, if either, exhibit diminishing marginal returns to labor?

At L = 4 and K = 4, the marginal product of labor is 2 and the marginal product of capital is 3. What is the marginal rate of technical substitution (MRTS)?

Answer 1

The optimal bundle is that where MRT =MRS

MRT=-price ratio=-pz/pb=-(10/5)=-2{ just look at MRS ,it shows additional QUANTITY of Z consumption and substitute of B . So price of Z will be in numerator and price of B in denominator}

MRS=MRT

-3B/Z=-2

3B=2Z

B=2z/3

Putting this optimal condition into budget constraint,

500=5*2z/3+10z=40z/3

500*3/40=z

Z=37.5

B=2*37.5/3=75/3=25

K=2

a) q=5L+2

Marginal product of labour=∆q/∆L=5

Constant return to scale

b)q=L^0.5*2^0.5

∆q/∆L=2^0.5/(2*L^0.5)

As L is in denominator ,as we increase L Marginal product of labour decreases.

So part b) exhibit diminishing marginal return to labour

MRTS=Marginal product of labour/ Marginal product of capital=2/3