Problem 3
Suppose that a person regards ham and cheese as pure complements - he or she will always use one slice of ham in combination with one slice of cheese to make a ham and cheese sandwich. Suppose also that ham and cheese are the only goods that this person buys and that bread is free. a. If the price of ham is equal to the price of cheese, show that the own- price elasticity of demand for ham is -0.5 and that the cross-price clasticity of demand for ham with respect to the price of cheese is also -0.5 b. Explain why the results from part (a) reflect only income effects, not substitution cffccts. What are the compensated price elasticities in this problem? c. Use the results from part (b) to show how your answers to part (a) would change if a slice of ham cost twice the price of a slice of cheese. d. Explain how this problem could be solved intuitively by assuming this person consumes only one good - a ham-and-cheese sandwich.
Problem 6
David \(\mathrm{N}\). gets \(\$ 3\) per week as an allowance to spend any way he pleases. Because he likes only peanut butter and jelly sandwiches, he spends the entire amount on peanut butter \(\langle\text { at } \$ 0.05 \text { per ounce })\) and jelly (at \(\$ 0.10\) per ounce). Bread is provided free of charge by a concerned neighbor, David is a particular catcr and makes his sandwiches with exactly 1 ounce of jelly and 2 ounces of peanut butter. He is set in his ways and will never change these proportions. a. How much peanut butter and jelly will David buy with his \(\$ 3\) allowance in a week? b. Suppose the price of jelly were to rise to \(\$ 0.15\) an ounce. How much of each commodity would be bought? c. By how much should David's allowance be increased to compensate for the rise in the price of jelly in part (b)? d. Graph your results in parts (a) to (c). e. In what sense does this problem involve only a single commodity, peanut butter and jelly sandwiches? Graph the demand curve for this single commodity. f. Discuss the results of this problem in terms of the income and substitution effects involved in the demand for jelly.
Problem 13
Consider a simple quasi-linear utility function of the form \(U(x, y)=x+\ln y\) a. Calculate the income effect for each good. Also calculate the income clasticity of demand for each good. b. Calculate the substitution effect for each good. Also calculate the compensated own-price elasticity of demand for each good. c. Show that the Slutsky equation applies to this function. d. Show that the elasticity form of the Slutsky equation also applies to this function, Describe any special features you observe.
