1 Assist kindly...

Exercise 1.2.3 a) Suppose there are two goods in a market, and that you buy ql of the first and q2 of the second. Give a mathematical expression for the total cost. b) Now, use the answer to a) to show that the marginal rate of transformation, MRT, is equal to the slope of the budget line. 1.3 Utility Maximization Exercise 1.3.1 a) Explain briefly, what utility maximization is. b) What is a utility function? c) What is the criterion that a consumer maximizes her utility? Give the answer in the form of a mathematical expression. Exercise 1.3.2 a) Suppose a consumer has two goods from which to choose. Draw a graph, with quantities on the X- and Y-axes, that illustrates how she can choose, given prices and income. b) Also, illustrate a few indifference curves in the graph. c) Show how the consumer maximizes her utility and where in the graph this occurs. d) Can you give an example of a situation in which the consumer will find more than one point where she maximizes her utility? Think about what the indifference curves must look like to make this possible. Exercise 1.3.3 Look at Figure E.1.I again. Suppose the consumer maximizes her utility at A, and that the price of good 2 is 100. What is the price of good 1? How large is the consumer's income?Exercise 1.2.1 a) Explain in words what the budget line is. b) Suppose we have two goods. The price of good I is 10 and the price of good 2 is 15. The income is 30. Construct a diagram, with the quantities on the X-and Y-axes, and draw a budget line in the diagram. c) How do the prices and the income affect the shape of the graph? What happens if the price of one good rises? What happens if income increases? Exercise 1.2.2 a) State the definition of the marginal rate of transformation, MRT. Explain what it means in words. b) Calculate MRT in Exercise 1.2.1.1. (20 points) Consider the Bertrand duopoly model with homogeneous products. Suppose that the quantity that consumers demand from i is a - pi when p p,, and (a-p.)/2 when p. = p,. Suppose also that there are no fixed costs and that marginal costs are constant at c, where c