Elementary Mathematical Techniques for Economics

Instructor: Ram Sewak Dubey ECON 317: Problem Set 5 November 1, 2018

1. [Marginal, Average and Total Concepts - I]

Find the marginal and average functions for each of the following total functions and evaluate them at Q = 3 and Q = 5.

(a) Total Cost Function (TC) TC = 3Q2 +7Q+12.

(b) Total Profit Function (π) π = Q2 −13Q+78.

(c) Total Revenue Function (TR) T R = 12Q−Q2.

(d) Total Cost Function (TC) TC = 35+5Q−2Q2 +2Q3.

2. [Marginal Expenditure Function]

Find the marginal expenditure (ME) functions for each of the following supply functions and evaluate them at Q = 4 and Q = 10. Hint: To find the ME function, we need to find the total expenditure function given the supply function and then takes it’s derivative with respect to Q.

(a) Supply Function P = Q2 +2Q+1.

(b) Supply Function P = Q2 +0.5Q+3.

3. [Marginal Revenue Function]

Find the marginal revenue (MR) functions for each of the following demand functions and evaluate them at Q = 4 and Q = 10.

(a) Demand Function Q = 36−2P.

(b) Demand Function 44−4P−Q = 0.

4. [Marginal Propensity to Consume]

Find the marginal propensity to consume (MPC = dC/dY ) for each of the following consumption functions.

Submission deadline: November 7, 2018 in class Page 1 of 2

Instructor: Ram Sewak Dubey ECON 317: Problem Set 5 November 1, 2018

(a) C =C0 +bY.

(b) C = 1200+0.8Yd , Yd = Y −T, and T = 100.

(c) C = 2000+0.9Yd , Yd = Y −T, and T = 300+0.2Y.

5. [Marginal Cost]

Find the marginal cost (MC) functions for each of the following average cost functions.

(a)

AC = 1.5Q+4+ 46 Q .

(b)

AC = 160 Q

+5−3Q+2Q2.

(c) AC = Q2 −4Q+174.

6. [Marginal Product]

Find the average product (APL) and marginal product (MPL) functions for the following total product func- tion.

(a) T P = 90L2 −L3.

(b) T P = aL+bL2 − cL3, (a > 0,b > 0,c > 0).

7. [Marginal Revenue for Linear Demand]

(a) Plot the the linear inverse demand curve P = 60−3Q. (b) Find the total revenue and the marginal revenue function mathematically.

(c) Compare the slope of the inverse demand curve and the marginal revenue curve.

(d) BONUS Provide a mathematical proof for the general result that given a linear inverse demand curve, the marginal revenue curve must have the same vertical intercept but will be twice as steep as the inverse demand curve.

Submission deadline: November 7, 2018 in class Page 2 of 2