Question 1. In a basic Keynesian macroeconomic model it is assumed that Y = C + I where
I = 820 and C = 60 + 0.8Y.
What is the marginal propensity to consume?
What is the equilibrium level of Y?
What is the value of the multiplier?
What increase in I is required to increase Y to 5,000?
If this increase takes place will savings (Y - C) still equal I
Question 2. A firm faces the demand function p = 190 - 0.6q and the total cost function
TC = 40 + 30q + 0.4q2
What output will maximize profit?
What output will maximize total revenue?
What will the output be if the firm makes a profit of £4,760?
Question 3. A firm faces the demand schedule q = 40 - p0.5 (where p0.5≥ 0, q ≤ 40) and the cost schedule
TC = q3- 2.5q2+ 50q + 16. What price should it charge to maximize profit
If TC = 0.5q3- 3q2+ 25q + 20 derive functions for:
a. MC
b. AC,
c. the slope of AC.
Question 5. Find whether any stationary points exist for the following functions for positive values of q, and say whether or not the stationary points are at the minimum values of the function.
AC = 345.6q-1+0.8q2 4
AC = 600q-1+0.5q1.5 4
MC = 30+0.4q2 4
TC = 15+27q -9q2+q3 4
MC = 8.25q 2
Question 6. Constrained optimization problem.
A consumer achieves a certain level of satisfaction from consumption of different quantities of apples and bananas according to the following indifference curve:
.B=5+2W-?W/2?^2
Where a = quantities of apples consumed per day; and
b = quantities of bananas consumed per day
if the price of apples is 5 cents and the price of banana is 4.5 cents each, at what combination of apples and bananas will this consumer achieve his given level of satisfaction at least cost?
Question 7. Unconstrained optimization problem.
An entrepreneur producing shoes uses a single variable input, leather, which he can purchase for $9 per unit. Each pair of shoes sells for $6.
There is perfect competition in both product and factor markets. The production function for the process is
.y=30x^0.5
y = output of shoes in pair; and
x = input of leather in units
Derive a function showing this entrepreneur's net revenue function as a function of leather input.