a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q. (i) Derive an expression, R (q) for Teddy J′s total revenue curve. (ii) Derive an expression, Π (q) for Teddy J ′ s profit function. (iii) Determine whether Teddy J′s profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid. (iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profit.
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(a) Teddy J is a manufacturer of dish washing liquid. If his monthly demand function for 750ml size is q = 4000 − 250p and his total cost function is C(q) = 500 + 0.2q.
(i) Derive an expression, R (q) for Teddy J′s total revenue curve.
(ii) Derive an expression, Π (q) for Teddy J ′ s profit function.
(iii) Determine whether Teddy J′s profit is increasing or decreasing when he produces 5 hundred, 750ml bottles of dish washing liquid.
(iv) How many 750ml bottles of dish washing liquid should Teddy J produce per month if he wishes to maximize his profit.
(b) A firm has an average cost function
A (q) = 125 q + q 2 16 − 4.
Where q is the firm output.
- Determine the level of output for average costs at minimum.
- Hence determine the range of values for which average costs are decreasing.
- What part of the decreasing range is practically feasible?
(iv) Write an equation for the total cost function.
(v) Hence calculate the level of output for which total costs at minimum.
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