Elementary Mathematical Techniques For Economics | Buy Assignments Online
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
