Question

Consider a competitive exchange economy with two individuals (A and B) and two goods ( F and W ). The total endowments of F and W are 10 each. Consumer A has the following utility function: u A =FW while consumer B has preferences such that she must have one unit of F for every unit of W. (a) Derive an expression for the contract curve and illustrate in an Edgeworth box diagram. (b) What is the relative price of F,P F /P W, in a competitive equilibrium? (c) Now suppose that consumer B's utility function is u B=F+2W Let consumer A's utility function remain unchanged. Derive an expression for the contract curve now and illustrate in a new Edgeworth box diagram. (d) What is the relative price of F,P F /P W, in a competitive equilibrium?

Answer 1

(a) To derive the expression for the contract curve, we need to find the points where the indifference curves of consumers A and B are tangent to each other. Let's denote FA as the amount of F consumed by consumer A, and FB as the amount of F consumed by consumer B. Similarly, let's denote WA as the amount of W consumed by consumer A, and WB as the amount of W consumed by consumer B. Since the total endowments of F and W are 10 each, we have FA + FB = 10 and WA + WB = 10.

Step-by-step explanation:

(a) To derive the expression for the contract curve, we need to find the points where the indifference curves of consumers A and B are tangent to each other. Consumer A's utility function is uA = FW, while consumer B's utility function is uB = min(F,W). We need to solve for F and W such that they satisfy consumer A's utility function and consumer B's preferences. Let's denote FA as the amount of F consumed by consumer A, and FB as the amount of F consumed by consumer B. Similarly, let's denote WA as the amount of W consumed by consumer A, and WB as the amount of W consumed by consumer B. Since the total endowments of F and W are 10 each, we have FA + FB = 10 and WA + WB = 10. From consumer A's utility function, we can express FA in terms of WA: FA = uA/WA = (FWA)/WA = F. Similarly, from consumer B's preferences, we can express FB in terms of WB: FB = min(FB, WB) = FB. Since FA + FB = 10, we have F + FB = 10. Solving this equation along with the equation WA + WB = 10 will give us the values of F and W that satisfy the given conditions. We can plot these points in an Edgeworth box diagram to illustrate the contract curve.