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The economist for the Grand Corporation has estimated the company’s cost function, us-
ing time series data, to be where TC 5 Total cost
TC=50+16Q-2Q2 +0.2Q3 Q 5 Quantity produced per period
- Plot this curve for quantities 1 to 10.
- Calculate the average total cost, average variable cost, and marginal cost for these quan-
- tities, and plot them on another graph.
- Discuss your results in terms of decreasing, constant, and increasing marginal costs.
- Does Grand’s cost function illustrate all these?
Company uses a 10% interest rate for all capital expenditures and has done the following analysis for four projects for the upcoming year:
Project A
Initial capital outlay $200,000
Annual net cash inflows Year1 65,000 - Year2 70,000 - Year3 80,000 - Year4 40,000
Project B
Initial capital outlay $298,000
Annual net cash inflows Year1 100,000 - Year2 135,000 - Year3 90,000 - Year4 65,000
Project C
Initial capital outlay $248,000
Annual net cash inflows Year1 80,000 - Year2 95,000 - Year3 90,000 - Year4 80,000
Project D
Initial capital outlay $272,000
Annual net cash inflows Year1 95,000 - Year2 125,000 - Year3 90,000 - Year4 60,000
a) You are required to select one of the above projects using Accounting Rate of Return; Payback Period; Net Present Value.
b) Which project(s) company should undertake using NPV if it has 500,000 funds available?
What are the individual Supply and Market Supply? schedule and the demand curve, and how are they related? Why does the demand curve slope downward?
Do each of a-d, both geometrically (you need not be precise) and using calculus. There are only two goods; x is the quantity of one good and y of the other. Your income is I and u(x,y) = xy + x + y.
(a) Px = $2; Py = $1; I = $15. Suppose Py rises to $2. By how much must I increase in order that you be as well off as before?
(b) In the case described in part (a), assuming that I does not change, what quantities of each good are consumed before and after the price change? How much of each change is a substitution effect? How much is an income effect?
(c) Px = $2; I =$15. Graph the amount of Y you consume as a function of Py , for values of Py ranging from $0 to $10 (your ordinary demand curve for Y).
(d) With both prices equal to $1, show how consumption of each good varies as I changes from $0 to $100.
Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively.
Now a government subsidy program lowers the price of X from $20 per unit to $10 per unit.
(e) Calculate and graphically show the change in good X consumption resulting from the program.
(f) Graphically show the change in consumption attributable to the separate income and substitution effects.
(g) Show (graphically) how much the program cost the government.
Stuart's utility function for goods X and Y is represented as U(X,Y)=X0.8Y0.2. Assume that his income is $100 and the prices of goods X and Y are $20 and $10, respectively.
(a) Express his marginal rate of substitution (MRS) between goods X and Y. As the amount of X increases relative to the amount of Y along the same indifference curve, does the MRS increase or decrease? Explain.
(b) What is his optimal consumption bundle (X*, Y*), given income and prices of the two goods?
(c) How will this bundle change when all prices double and income is held constant? When all prices double AND income doubles?
(d) Derive the demand curve for good X and demand curve for good Y.
Do each of a-d, both geometrically (you need not be precise) and using calculus. There are only two goods; x is the quantity of one good and y of the other. Your income is I and u(x,y) = xy + x + y.
(a) Px = $2; Py = $1; I = $15. Suppose Py rises to $2. By how much must I increase in order that you be as well off as before?
(b) In the case described in part (a), assuming that I does not change, what quantities of each good are consumed before and after the price change? How much of each change is a substitution effect? How much is an income effect?
(c) Px = $2; I =$15. Graph the amount of Y you consume as a function of Py , for values of Py ranging from $0 to $10 (your ordinary demand curve for Y).
(d) With both prices equal to $1, show how consumption of each good varies as I changes from $0 to $100.
Robinson's preferences between apples (a) and bananas (b) are expressed by the following:
U = (a+2)0.5(b+1)0.5
(a) Show that Robinson's indifference curves are negatively sloped.
(b) Are they convex to the origin? Explain.
Discuss how changes in demand can change equilibrium price
Robinson's preferences between apples (a) and bananas (b) are expressed by the following:
U = (a+2)0.5(b+1)0.5
(a) Show that Robinson's indifference curves are negatively sloped.
(b) Are they convex to the origin? Explain.
