Assignment:
1. A firm's estimated demand curve for its product is represented by the equation:
where is the quantity sold per year and is the price per unit.
(a) Based on the estimated demand curve, write the equations for the firm's
(i) total revenue
(ii) average revenue
(iii) marginal revenue
(b) What is the maximum total revenue per year that the firm can obtain from sales of its product? (Give the exact dollar amount and show how you determined it.)
(c) Calculate the point price elasticity of demand for the firm's product when. Is the demand elastic or inelastic at that quantity? How do you know?
2. Suppose a market is characterized by the following estimates of demand and supply:
(a) Find the equilibrium price and quantity? Graph your solution.
(b) How much is the consumer surplus?
(c) Suppose a $2 excise tax is levied on this good. What will happen to the equilibrium price and quantity? Show the changes in your graph from part (a).
(d) How much is the consumer surplus after the tax?
(e) How much tax revenue does the government earn with the $2 tax?
3. Empirical data for the US have shown that medical costs have increased more rapidly than other prices. You are asked to show how rising medical costs have affected consumer alternatives. Suppose X represents the quantity of medical services, and Y represents the quantity of other goods. in addition, let income (M) be measured in hundreds of dollars, the price of medical services and other goods in terms of dollars per minute, with M = 150, PX = 5, and PY =
(a) Graph the budget line. Determine the market rate of substitution.
(b) In your graph show the budget set.
(c) If PX doubles, what happens to the budget constraint. Show this effect in your graph.
(d) What is the meaning of the slope of the two budget constraints?
4. The following table summarizes the total costs for a specific firm. Based on this information, fill in the missing entries in the table for fixed cost, variable cost, average fixed cost, average variable cost, average total cost, and marginal cost. Show how you obtain each category of cost.
|
Q
|
FC
|
VC
|
TC
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AFC
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AVC
|
ATC
|
MC
|
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0
|
|
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1,000
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|
|
|
|
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10
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|
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2,000
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|
|
|
|
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20
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|
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2,500
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|
|
|
|
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30
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|
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4,000
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|
|
|
|
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40
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|
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6,000
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|
|
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|
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50
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|
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10,000
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|
|
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|
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60
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|
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15,000
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|
5. The table below summarizes the short-run production function for your firm. Your product sells for $10 per unit, labor costs $40 per unit, and the rental price of capital is $10 per unit. Complete the following table, and then answer the accompanying questions.
|
L
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K
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Q
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MPL
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APL
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APK
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VMPL
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0
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5
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0
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|
|
|
|
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1
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5
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20
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|
|
|
|
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2
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5
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60
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|
|
|
|
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3
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5
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120
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|
|
|
|
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4
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5
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160
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|
|
|
|
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5
|
5
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180
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|
|
|
|
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6
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5
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190
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|
|
|
|
|
7
|
5
|
190
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|
|
|
|
|
8
|
5
|
180
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|
|
|
|
|
9
|
5
|
160
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|
|
|
|
|
10
|
5
|
120
|
|
|
|
|
|
11
|
5
|
60
|
|
|
|
|
(a)Which inputs are fixed inputs? Which are the variable inputs?
(b)How much are your fixed costs?
(c)What is the variable cost of producing 40 units of output? Assume that L is indivisible, (that is, it must be hired in an integer number of units).
(d)How many units of the variable input should be used to maximize profits?
(e)What are your maximum profits?
(f) Over what range of variable input usage do increasing marginal returns exist?
(g)Over what range of variable input usage do decreasing marginal returns exist?
(h)Over what range of variable input usage do negative marginal returns exist?