ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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Show full answers and steps to part d) e) & f)
**Exercise 5:**

Ron’s Window Washing Service is a small business that operates in the perfectly competitive residential window washing industry in Evanston, Illinois. The short-run total cost curve is \( STC(q) = 40 + 10q + 0.1q^2 \), where \( q \) is the number of windows washed per day. All fixed costs are sunk (unrecoverable).

**a)** Find Ron’s short-run marginal cost curve, \( SMC(q) \), and average variable cost curve, \( AVC(q) \).

**b)** How many units of output should Ron produce each month to maximize profits if the market price is \( p = \$20 \)? [Hint: Use the profit-maximizing condition]

**c)** What is Ron’s maximum monthly profit? [Hint: Use the profit function]

**d)** What is the level of output corresponding to the minimum level of Ron’s average variable cost curve? [Hint: At the minimum level of the average variable cost curve, it crosses with the short-run marginal cost curve. Set \( AVC(q) = SMC(q) \) and solve for \( q \)]

**e)** Find Ron’s shutdown price. [Hint: The shutdown price when all fixed costs are sunk is given by the minimum level of the average variable cost curve. Plug the value of \( q \) you found in part (d) into the \( AVC(q) \). You have found the shutdown price for Ron]

**f)** Find Ron’s short-run supply curve. [Hint: Use the shutdown price found in part (e). Ron supplies the profit-maximizing quantity when price is equal or higher than the shutdown price, and zero otherwise]
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Transcribed Image Text:**Exercise 5:** Ron’s Window Washing Service is a small business that operates in the perfectly competitive residential window washing industry in Evanston, Illinois. The short-run total cost curve is \( STC(q) = 40 + 10q + 0.1q^2 \), where \( q \) is the number of windows washed per day. All fixed costs are sunk (unrecoverable). **a)** Find Ron’s short-run marginal cost curve, \( SMC(q) \), and average variable cost curve, \( AVC(q) \). **b)** How many units of output should Ron produce each month to maximize profits if the market price is \( p = \$20 \)? [Hint: Use the profit-maximizing condition] **c)** What is Ron’s maximum monthly profit? [Hint: Use the profit function] **d)** What is the level of output corresponding to the minimum level of Ron’s average variable cost curve? [Hint: At the minimum level of the average variable cost curve, it crosses with the short-run marginal cost curve. Set \( AVC(q) = SMC(q) \) and solve for \( q \)] **e)** Find Ron’s shutdown price. [Hint: The shutdown price when all fixed costs are sunk is given by the minimum level of the average variable cost curve. Plug the value of \( q \) you found in part (d) into the \( AVC(q) \). You have found the shutdown price for Ron] **f)** Find Ron’s short-run supply curve. [Hint: Use the shutdown price found in part (e). Ron supplies the profit-maximizing quantity when price is equal or higher than the shutdown price, and zero otherwise]
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