Intermediate Microeconomics · free preview
The Competitive Firm and Profit Maximization
A price-taking firm treats output price and input prices as given, maximizes profit p f of x minus w x, and the first-order condition p times MP equals w equates the input's marginal revenue product to its wage, the whole firm-side optimization in one equation.
1. Price taker
Price taker
2. The marginal condition
The marginal condition
3. Two readings of one condition
Two readings of one condition
4. Long run versus short run again
Long run versus short run again
5. The price-taking assumption
What makes a firm a price taker in the competitive model?
6. The marginal condition
The one-input profit-maximization first-order condition is which equation?
7. Working the example
For f equal to root x, p of 10, w of 2, what is the optimal input?
8. The supply-side reading
Rearranged as p equals w over MP, the condition says what?
9. Revenue at the optimum
For the worked example, compute revenue p times y at the optimum, and write the number.
10. Profit at the optimum
Subtract cost 2 times 6.25 from revenue 25, and write the profit.
11. Output at the optimum
In the worked example f equal to root x with p of 10 and w of 2, the optimal input is 6.25. What output follows?
12. The margin at the optimum
At the optimum, what does the marginal product equal in the worked example?
13. A higher price
The price rises to 12 with the wage still 2. What are the new optimal input and output?
14. A dearer input
The wage rises to 3 with the price still 10. What happens to the optimal input?
15. Output at the higher price
With p of 12 and w of 2, compute the optimal output, and write the number.
16. Profit at the higher price
At p of 12 with the optimum (9, 3), compute profit as revenue 36 minus cost 18, and write the number.
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