1) A consumer's utility function is given by

U(x1, x2) = 2x1 x2 + 3x1

where x1 and x2 denote the number of items of two goods G1 and G2 that are bought. Each item

costs $1 for G1 and $2 for G2.

What is the "marginal rate of substitution", x1/ x2 ?

(10 points)

2) Suppose that your grade on this examination is described by G = 2.5A0.5E0.5, where G is your

numerical score, A is ability, and E is effort measured in terms of hours studied.

What is A/E ?

3) For the following equations, find the specified derivative. find dy/dx.

(20 points)

i) x2+3xy+5y2=23

(20 points)

ii) 40price+7pricequantity+quantity=2000. Find d(price)/d(quantity).

(Note: quantity is the square root of quantity)

(20 points)

iii) 1000=5L0.6 K0.4

. Find dK/dL.

(20 points)

iv) The production function for a widget factory is 1000=15L0.7 K0.3

.

Find dK/dL and dL/dK. Interpret what they mean.