Search & Filtering
- Assume that Roberts’s utility from consuming good X and good Y is given by the following function:
U = X0.3Y0.7
Where X is the quantity of good X while Y is the quantity of good Y.
Assume the price of X (PX) is £25, the price of Y (PY) is £35 and he has a budget of £1000 to spend on the two goods.
c. Using the demand functions, calculate the quantities of X and Y Robert should purchase to maximise his utility. Calculate the utility this optimal consumption bundle provides.
(a) At what price and quantity will total revenue be maximized?
Assume that the budget constraint is given by the equation Q1 = 1,000 – 5Q2, where Q1 and Q2 represent quantities of two goods. Normally, indifference curves are convex to the origin, but assume in this case that they are linear with a constant slope of –2.
i) Graph the budget constraint (with Q1 on the vertical axis).
ii) Draw in a set of indifference curves and label the utility-maximizing point.
iii) Where would the utility-maximizing point have been if the indifference curves had a constant slope of –6?
a) Draw an indifference curve (one IC is enough) that represents this person’s preferences. Please label the graph properly including values for x and y.
b) Intuitively, and without formally solving, can you guess the maximized values x* and y* for the above utility function. Explain your answer.
c) Derive the optimal values x*and y* by formally solving the above utility function subject to the above constraint. You can use any of the utility maximization techniques we learned in class.
d) Compare your answers in parts b) and c). Based on the utility function that is given in this problem as well as the budget constraint, can you explain the differences between the answers
axis and P is on the horizontal axis. Then transform these equations so P is expressed in
terms of Q and plot these transformed equations on a graph in which P is on the vertical
axis and Q is on the horizontal axis.
a. Q = 250 - 10P
b. Q = 1,300 - 140P
c. Q = 45 - 0.5P
A. All firms are price takers.
B. All firms produce where average costs are minimised.
C. The equilibrium level of output occurs where marginal cost equals marginal revenue.
D. All buyers and sellers have perfect knowledge of market conditions.
E. All sellers act independently of each other.
What conclusions for antitrust policy are suggested by your answer?
