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Production and Costs: Profit Maximization. AP Economics Mr. Bordelon. Maximizing Profit. What quantity of output would maximize producer’s profit? Find profit-maximizing quantity by calculating total profit for each amount for comparison.
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Production and Costs:Profit Maximization AP Economics Mr. Bordelon
Maximizing Profit • What quantity of output would maximize producer’s profit? • Find profit-maximizing quantity by calculating total profit for each amount for comparison. • Use marginal analysis to determine the optimal output. • Total Revenue • TR = PQ • Profit • π = TR - TC
Joslyn Farms Market price is $18. Total Cost is a given. At each quantity, profit changes, first increasing, and then decreasing. At what quantity is profit maximized?
Marginal Analysis to Choose Profit-Maximization Quantity of Output • Translation: Marginal analysis helps us pick the maximum amount of profit we can make with a particular amount of production. • Principle of marginal analysis. Every activity should continue until marginal benefit equals marginal cost. • We’ve seen this again and again now, between marginal utility per dollar, marginal product of labor vs. capital, marginal cost = average total cost. We are now establishing this principle. • Marginal Revenue. Change in total revenue generated by additional unit of output. • MR = ΔTR/ΔQ
Marginal Analysis cont’d • Optimal output rule. Profit is maximized by producing the quantity of output at which marginal revenue of the last unit produced is equal to its marginal cost. MR = MC. • Reality Check. In real life, there may not be any specific quantity where MR = MC. In that case, the producer should produce until one ore unit would cause MR to fall below MC.
Marginal Analysis cont’d. Marginal cost initially decreases as output increases. Then MC begins to increase, giving MC the swoosh shape we’re used to. MR is assumed to be true for every level of output here, which is true in perfectly competitive markets. What would be the profit-maximizing output here, and why?
Marginal Analysis cont’d. Marginal cost initially decreases as output increases. Then MC begins to increase, giving MC the swoosh shape we’re used to. MR is assumed to be true for every level of output here, which is true in perfectly competitive markets. 5 tomatoes. Net gain stays positive upwards through 5. 6 and 7, and after, are all negative. 5 tomatoes is the level of output at which MC = market price of $18. Think we could graph this out?
Marginal Analysis cont’d. Hey, it’s our MC curve that we all know and love! And it brought a friend, the MR curve! MR curve shows how MR changes as output changes. MR stays the same in this particular hypothetical because we’ve assumed that MR is constant. It may not always be so. Notice that the MR and MC curves intersect at 5 tomatoes, whereMC = MR.
When is Production Profitable? • Should I produce at all? • This is where economic profit comes in. Whether I bother to produce a product or not, to stay in business or close down permanently, is based on economic profit. • Whether or not a business is profitable depends on the market price whether selling the firm’s optimal quantity of output at the market price results in at least a normal profit. • If so, then how much? • Marginal analysis Profit-Maximizing Quantity of Output
Katie and Dagny’s Lemonade Stand • Market price is $2 per cup. Katie and Dagny want to sell the quantity of lemonade that maximizes their profits.
Katie and Dagny’s Lemonade Stand When does profit stop increasing?
Katie and Dagny’s Lemonade Stand Profit stops increasing at the 9th cup. Production should stop at the 8th cup. Why 8 and not 7 cups?
Katie and Dagny’s Lemonade Stand Profit stops increasing at the 9th cup. Production should stop at the 8th cup. Production should stop at 8 cups because profit is $6 at both levels of output. In that case, a business will choose the larger of the two (real life reason).
Katie and Dagny’s Lemonade Stand • Katie and Dagny start asking whether they should produce yet another cup of lemonade. If the additional money coming into the firm as revenue is more than the dollars going out as cost, then yes, they should. • MR = ΔTR/ΔQ • MC = ΔTC/ΔQ • Notice mathematically, that if Q changes on unit at a time: • MR = ΔTR • MC = ΔTC
Katie and Dagny’s Lemonade Stand TR increases by $2 every time another cup of lemonade is made. TC increases by larger amounts, as MC increases as more units are produced (why is MC doing that?) In this case, Katie and Dagny will never produce the 9th unit because additional dollars coming in as MR are less than additional dollars going out as MC. 1-7 cups: MR > MC Yes profits increase 9-10 cups: MR < MC No profits decrease
Katie and Dagny’s Lemonade Stand 1-7 cups: MR > MC Yes profits increase 9-10 cups: MR < MC No profits decrease Production should stop at the 8th cup whereMR = MC. This is the optimal output rule for profit maximization.
Katie and Dagny’s Lemonade Stand Katie and Dagny are enjoying economic profits. At the price of $2 per cup, TR of 8 cups is more than total economic cost of producing the 8 cups. As long as economic profit is more than or equal to zero (normal profit), the lemonade stand should stay open. If it were to drop below zero, Katie and Dagny should go do something else more valuable.
