Joe consumes two goods, food (x) and clothing (y). His utility function is given by U=x^(1/2) y^(1/2)
Does Joe have a diminishing marginal utility for each good?
Does the assumption of ‘more is better' hold for Joe? Explain.
Derive Joe's demand for food as a function of the price of food(? p?_x), the price of clothing (? p?_y), and income (I). Do the same for clothing.
Find the own price elasticity of demand for food. Is demand for food elastic? Explain.
Find the income elasticity of demand for food. What kind of good is food?
Assume I=$400, ? p?_x=$10, and ? p?_y=$10. Find the quantity demanded of food and clothing. What is Joe's level of utility at this optimal basket?
On a graph with food on the horizontal axis and clothing on the vertical axis, draw the indifference curve corresponding to the level of utility obtained in part f. Show the optimal basket on the graph. On the same graph, draw the budget line given in part f
Let the price of clothing rise to? p?_y=$40. Given the same income and the same price of food as in part f, find the quantity demanded of food and clothing. What is the level of utility now?
If the government wanted to compensate Joe for his loss of utility, how much should his income be raised so that he could achieve the same level of utility as in part f?