2. P2: Economic Applications of Functions and Derivatives a. A firm's short run total cost function is TC = 0.5q² +q+500. The firm sells in a perfectly competitive market and the ruling price is p = 61. b. Find the most profitable level of output, and the profits at that output. c. Sketch the graphs of total cost and total revenue with the same axes, and do the same with marginal cost and marginal revenue. Sketch the graph of the profit function. Indicate in all diagrams the equilibrium values of the variables.
2. P2: Economic Applications of Functions and Derivatives a. A firm's short run total cost function is TC = 0.5q² +q+500. The firm sells in a perfectly competitive market and the ruling price is p = 61. b. Find the most profitable level of output, and the profits at that output. c. Sketch the graphs of total cost and total revenue with the same axes, and do the same with marginal cost and marginal revenue. Sketch the graph of the profit function. Indicate in all diagrams the equilibrium values of the variables.
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.4P
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Question
Solve number 1d. And no. 2-3
Transcribed Image Text:1. P1: Economic Applications of Functions and Derivatives
a. Sketch the graph of the short run total cost function TC = 3q² +5g +300, for
q=0 to q = 15;
b.
Find the marginal and average cost functions. Sketch their graphs.
c. Explain in words why average cost is greater than marginal cost at all levels of
output;
d. How does the difference between marginal and average cost, MC – AC,
behave as 9 increases without limit?
2. P2: Economic Applications of Functions and Derivatives
a. A firm's short run total cost function is TC = 0.5q² +q+500. The firm sells in
a perfectly competitive market and the ruling price is P = 61
b. Find the most profitable level of output, and the profits at that output.
c. Sketch the graphs of total cost and total revenue with the same axes, and do the
same with marginal cost and marginal revenue. Sketch the graph of the profit
function. Indicate in all diagrams the equilibrium values of the variables.
3. P3: Elasticity
a. Using the demand function: Q = -3p²+2p+ 1965. Find the total revenue
and marginal revenue functions (as functions of q).
b. Find the point elasticity (1) when P = 10; (2) when P = 24.
c. Sketch the demand function.
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