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The figure above shoes a Cobb-Douglas utility function of the form . The budget line is represented by . The optimum point of consumption is where the indifference curve and the budget constraint are tangent.
The slope of the indifference curve is given by . By rearranging, we can write . This can be further re-written as:
Practice Questions by Economics Tutor
- Suppose that a consumer has a preference relation on R2 represented by the quasilinear utility function has income and faces prices and
- Derive the (Marshallian) demand
- Derive the indirect utility
- What is the marginal utility of income?
- Derive the expenditure
- Derive the Hicksian demand functions.
Cindy consumes two goods . Her preferences are represented by . The price of good is denoted by , the price of good is denoted by , and her income is denoted by 𝑚. Suppose Cindy gets a weekly allowance of £4. Suppose both goods are £2 per unit.
- Graph her budget constraint, and write down the equation of her budget line. In the same graph show Cindy’s indifference curves corresponding to the utility levels 𝑢, and . Solve for Cindy’s optimal consumption bundle and indicate it in your
- Derive her demand functions for good 1 and good 2 as functions of her income, , price of good 1, , and price of good 2, . Is good 1 normal or inferior? Ordinary or Giffen? Are goods 1 and 2 substitutes or complements?
- Suppose the price of good 1 rises to £4. How much would her parents have to increase her allowance in order to leave her exactly as well off as she was originally?
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