Calculate the equilibrium price and quantity, economics homework help

1.Suppose the following supply and demand functions represent the market for foreign made cars.

QS = 2p − 2

QD = 13 – p, where Q is the quantity in millions and p is the price measured in ten thousands (to be realistic).

a. Calculate the equilibrium price and quantity. Sketch the supply and demand curves on a graph. Show the equilibrium quantity and price.

b. Suppose the government imposes a quota of 6 million cars. Indicate the quota on the graph. Would that amount make the quota binding?

NOTE: BINDING MEANS THAT THE QUOTA (PRICE CEILING) WOULD BE EFFECTIVE AND WOULD serve the purpose (= MEANINGFUL FOR PRACTICAL PURPOSES).

c. Now suppose that the government imposes a price ceiling of $4 (ten thousands. That is, the realistic price is $40,000). Can $4 be the binding price ceiling?

d. Explain the relationship between the quota and the price ceiling specified in parts b) and c). USE THE GRAPH FOR CLUE.

• I heard on radio yesterday, 2/24/17 that ‘snapchat’ is encouraging advertisement makers to create ‘vertical’ instead of ‘horizontal’ ads (the mainstream ads that work better with TV). The reason being the vertical ads would fill the screen so that the users would be compelled to pay attention to the advertisements. Let us consider that the advertisement creators are considering this seriously.
• Suppose Monica decides to eat only steak and carrots on her dietician’s advice. A serving of steak gives 250 calories and 10 units of vitamins. A serving of carrots offers 100 calories and 30 units of vitamins. Monica’s doctor instructs her to get a maximum of 2000 calories and at least 150 units of vitamins.

Suppose that the utility function that describes the usefulness or benefit to the businesses from ‘horizontal advertisements, X’ (the traditional ones) and ‘vertical advertisements, Y’ is given by:

U(X,Y) = , where X and Y are measured in minutes.

Further, if the price of creating X is $1 million / minute, the price of Y is $4 million / minute, and the budget allocated [interpret this as income] for the advertisements is $1000 million.

• Write a monotonic transformation function for the utility function given above.
• Explain the purpose / the use of a monotonic transformed function in this context.
• Using the Lagrangian method to solve for the optimal quantities of X and Y. Write the optimum bundle.

NOTE: THE CALORIE CONSTRAINT AND VITAMIN CONSTRAINT ARE INEQUALITIES, BUT BOTH DO INCLUDE EQUALITY AS WELL.

• With ‘serving of carrots’ on horizontal axis and ‘servings of steak’ on vertical axis, draw BOTH the CALORIE constraint (= BUDGET) line, AND ‘VITAMIN’ (= BUDGET) line [USE at least 4 combinations of ‘steak’ and ‘carrots’].
• Shade all the bundles of carrots and steaks that satisfy both ‘calorie’ and ‘vitamin’ requirements (= AS CONSTRAINTS) suggested by the doctor.
• On the graph, draw an indifference curve that shows ‘carrots’ and ‘steak’ as complements. SHOW THE OPTIMAL BUNDLE OF CARROTS AND STEAKS.
• Suppose that Monica is not studying Microeconomics and thinks that ‘carrots’ and ‘steak’ are substitutable goods and therefore she is giving clues that the indifference curve is the usual convex shaped. Draw two different indifference curves – 1) that would make the optimal consumption bundle in favor of ‘steak’ and 2) the other optimal bundle that favors ‘carrots’. LABEL THE INDIFFERNCE CURVES APPROPRIATELY.
• Explain the shape of the realistic (based on doctor’s advice) indifference curve.

 

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