Q: Why is the tangent point special?

1. Q: Why is the tangent point special?

2. Q: Why is the tangent point special? A: It gives us a short cut.

3. Features of the tangency between isocost lines and isoquants. • Slope of isoquants is called the Marginal Rate of Technical Substitution (MRTS) • MRTS = MPL / MPK = (∆K / ∆L | Q=q) • At tangency, MRTS = input price ratio • MPL / MPK = w / r • MPK / r = MPL / w • (P* x MPK) / r = (P* x MPL) / w • Benefits-cost ratio is equal across inputs • Profit max’ing firm also sets benefits equal to cost, so r = MRPK and w = MRPL

4. Usefulness of shortcut: Finding firm’s optimal input choices • Recall that MPK / r = MPL / w • You will be given factor marginal products and factor prices • Firm must also achieve optimum for some cost level—recall the total cost equation • You will be given the target cost level • Can solve two equations for two unknowns • Optimal wage is even easier: one equation

5. Back to puzzle with shortcut: What happens if an input price changes? • To MRTS? • To input price ratio? • To market price? • To tangency between input price ratio and MRTS?

6. Lecture 18: Consumer Choice 1

7. Transition: The California Wine Producers • Is profit maximization a good assumption?

8. Transition: The California Wine Producers • Is profit maximization a good assumption? • What if your job makes you happy? • As a firm owner, you have lower costs • Opportunity costs are much lower because you’re doing something you like • Need utility theory to save profit maximization theory here

9. Start with the bottom line: Budget constraints • Consumers are simple: They consume and they work. • Consumption denoted c • Work denoted h • Consumers have only 24 hours per day in which to consume and work. • Wage for work denoted w • Price for consumption denoted p • Budget constraint?

10. Start with the bottom line: Budget constraints • Consumers are simple: They consume and they work. • Consumption denoted c • Work denoted h • Consumers have only 24 hours per day in which to consume and work. • Wage for work denoted w • Price for consumption denoted p • Budget constraint? p x c = w x h if h > 0; c = 0 if h = 0

11. Budget constraints summarize tradeoffs • A budget constraint in 2D can trade off any two goods • Our example: consumption and leisure • p x c = w x h • pc = 24w – w(24 – h) ; leisure = 24 – h = z • pc + wz = 24w = Imax • c = Imax / p- (w/p)z  A line! • A simpler example: A gift of $120,000 can be used to pay for college ($30k/year) or to buy cars ($20k/car)

12. Another budget constraint example

13. Budget definitions • Budget constraint: Requirement that expenditure on a set of goods equal available funds (income or endowment) • Budget set: All bundles of goods (points) that meet the BC, i.e. all feasible points • Budget line: All bundles of goods that meet the BC with equality

14. Indifference curves • Illustrate consumption bundles that give a consumer equal levels of utility • Drawn in consumption good space • U(c1, c2) = U(c3, c4) if the points (c1, c2) and (c3, c4) are both on the same IC • Consumer is “indifferent” between any two bundles on an indifference curve because all points on an IC provide the same utility

15. Features of indifference curves • Higher is better • Assumption that more is always better • “Local non-satiation” • Downward sloping • When decrease consumption of one good, must give more of the other to keep consumer happy • Convex • Results from diminishing marginal utility at higher levels of consumption for one good • Do not cross • Result of first assumption

16. Indifference curves, graphically

17. Assumptions forbid intersecting indifference curves

18. Marginal rate of substitution • MRS: The quantity of good 2 (y axis) that consumer must receive to remain indifferent to losing one unit of good 1 (x axis) • Equal to slope of an indifference curve at a given point • MRSYX = [∆Y/∆X | U = u*] = MUX/MUY • Varies with location on indifference curve • Not the same as elasticity!

19. MRS varies with location on indifference curve

20. The consumer’s optimization problem • Problem: Maximize utility subject to the budget constraint • In other words, achieve highest level of utility (IC) that intersects the budget line • Because of their curved shape, no two points on an indifference curve will be on the same budget line • At optimal bundle, MRSYX = MUX/MUY= PX/PY

21. The optimal bundle, graphically