1. Suppose that 10 years ago you purchased a car at $27,000 and the car was traded in today for $1,000. What is the depreciation rate? Suppose that the car is continuously discounting its value. (Show your work. This means that no work = no credit).

2. Consider the production function, Q = 15L3/4K1/4, where Q is output, L is labor input, and K represents capital input.

2-1) Using natural logarithms, transform this exponential function into a linear function.

2-2) Now assume that L = 10 and K = 5. What is the value of ln(Q)? Remembering that exp(ln(Q)) = Q, determine the value of Q.

3. Given the following system equations of price (P) and quantity (Q) determination in a widget market:

Demand: Q = 120 - 20P + 3G …..(1)

Supply: Q= 40 + 20P – 2N ……(2)

Where the price of substitute good, G = 200, and the cost of production N =100.

3-a) by using the repeated substitution method, please find P and Q.

3-b) if N is up by 20, show the impact of changing N on P and Q.

4. Consider the simplified national income model:

Y = C + I…………(1)

Where Y is GDP (national income), C is consumption, and I is investment. Consumption is determined by a behavioral equation, which in this problem takes the form

C= 3000+ 2/3Y……..(2)

Where Y and C are endogenous variables and Investment is exogenous, and, initially we assume

I =500……………….(3)

Determine the equilibrium level of national income (Y) and consumption (C) by using reduced form, and matrix algebra.

5. Consider the following system of equations:

6x1 + 2x2 – 3x3 = 10

2x1 + 4x2 + x3 = 0

x1 – x3 = 2.

Use Cramer’s rule to solve for the equilibrium values of x1, x2, and x3 in system of equations.

EC 202 Exam 3

1. Given y = x2

Please find (1) difference quotient, and

(2) the differential when x=2, dx =2

2. Show your work of differentiating the following 3 questions.

(This means that no workis no credit.)

a. Y = 12X2 - 6X + 4

b. Y = (5X + 1) * (x+ 4)

c. Y = (X + 4) / (X – 2)

3. Show your work of differentiating the following question.

Y = = 2 (7X2 – X) 4

4. Find the price elasticity of demand from the following function:

Qd = a– bP

2. Macroeconomics:

Consider the simplified, two-equation, national income model

Y = C + I + G

C = a + b Y

Where national income (Y) and consumption (C) are endogenous variables and investment (I) and government spending (G) are exogenous variables.

The parameters in the consumption function, where a represent the autonomous consumption expenditure and b represents the marginal propensity to consume, respectively.

2-a) Set up this model with a 2 x 2 matrix of coefficients matrix, a 2 x 1 vector of endogenous variables, and a 2 x 1 vector of constants (consider I + G to be one constant).

2-b) The model can be expressed as Ax = y, where A is the coefficient matrix, x is the vector of endogenous variable, and y is the vector of constants. Find the solution of x.

(You must show your work. This means that no work = no credit.)