Let a consumer, called Frank, have preferences described by the utility function: U = In (cl) + in (c2), where Cl is the consumption of c1commodities and c2 the consumption of c2commodities ("ln" refers here to the natural logarithm, remember that the derivative of ln(c) is 1!c). In the initial situation, Frank has 001 units of good 1 and 002 units of good 2 (these are his socalled endowments). The prices of the goods are given by p1 and p2 respectively. His income only consists of what he receives if he sells all his commodities at these prices. If Frank does not save, this means that his budget constraint is given by: plcl + p202 = pl 001 + p2w2 a now want to find Frank's demand for good 1 and good 2 as a function of prices and endowments. a. First formulate the Lagrangian using the utility function and budget constraint (denote the Lagrange multiplier by A). Then find the first- order conditions for CI and c2. You now have two expressions that you can combine to eliminateA. Show that p1c1=p202 holds. b. Substitute this in into Frank's budget constraint, and solve for CI. We now have the demand for CI as a function of prices and endowments. Also find the demand function for c2. c. What is the effect of increasing the endowment of good 1 on the demand for good 2? Explain your finding