Question

2. Assume Bob also likes pizza and going to the movies Assume the price of pizza is $10 per unit and the price of movie tickets is $10. Assume Bob's budget is $100. Assume Bob's initial equilibrium consumption point is point A that is labeled on the initial budget constrain in the diagram below. At point "A" Bob consumes 5 units of pizza and 5 units of movies at point A. The second budget constraint reflects an increase in Bob's budget to $200. Pizza •A(5,5) Movie Tickets 2a. Label the levels of pizza and movies associated with the X and Y intercepts for the two budget constraints in the above graph 2b. Assuming Bob's budget increases to $200, assume market basket "B" contains 4 pizzas and 16 movies and label point B on the budget constraint in the graph above. Next, indicated a market Basket C that contains 17 pizzas and 3 movies and label it in the graph above. Are pizzas and movies normal goods at points B and C? Explain! 2C. Derive the Income elasticity of demand for pizzas at point B. Use the arc elasticity formula and interpret your answer.

Answer 1

A).

Consider the given problem here there are two goods “X=Pizza” and “Y=Movies”. The price of “X” and “Y” are “$10”, => the equation of budget constraint is given by.

=> 10*X + 10*Y = 100, where “100” be the income of the consumer. The following fig shows the budget line of the consumer which is “A1B1”.

Y = Movies B (4, 16) A (5,5) C (17,3) > X = Pizza B1 B2 (10) (20)

B).

Let’s assume that the income of the consumer increases to “$200”, => the new budget line is “10*X + 10*Y = 200”. In the above fig the new budget line is “A2B2” and the “B” and “C” basket content different level of “X” and “Y”.

Now, from “A” to “B” the consumption of pizza decreases and the consumption of movie increases, => here “X=pizza” be the inferior good and “Y=movie” be the normal good. Similarly, from “A” to “C” the consumption of pizza increases and the consumption of movie decreases, => here “X=pizza” be the normal good and “Y=movie” be the inferior good.

C).

At point “A” the consumer consumes “5 units of pizza” and “5 units of movies”. At point “B” the consumer consumes “4 units of pizza” and “16 units of movies”. So, the income elasticity of demand for pizza is given below.

=> e = (dX/dM)*(M/X) = (4-5/200-100)*(200/4) = (-1/100)*(200/4) = (-2/4) = (-1/2).

=> e = (-1/2) < 0, here the income elasticity of demand is “-0.5”.