ECON

Consider the following quasilinear utility function: u(xy) = 3 x + 2 y, where x denotes the quantity of apples and y denotes the quantity of pears. Let income be m, the price for one apple be p, and the price for one pear be py. a) By applying the Lagrangian method, derive the ordinary demands for apples and pears. b) What is the impact of an increase in the price of apples on the ordinary demand for pears? What is the impact of an increase in income on the ordinary demand for apples? c Derive the Engel curve for apples. illustrate your answer in a carefully drawn Graph.

a. How will the additional supply of fish from another vendor affect the marginal costs and average total costs of production and profit-maximizing output level. Illustrate it graphically or numerically. Briefly explain your answer.

b. Will the modernization of the fish market (i.e., processes, replacement of fish porters, etc.) affect the market supply, equilibrium price and equilibrium quantity demanded of fish in the market? Briefly explain and illustrate it graphically.

Two firms produce the same good; y? denotes the output of firm 1 and y2 the output of firm 2. Production is free up to a maximum determined by capacity constraints. Producing above that level requires heavy investment and is therefore exceedingly expensive. Specifically, the total cost functions faced by the firms are: Clya)= 0 if y?s 7 and G{y) = 100 if y1> 7 for firm 1 Caly2)= 0 if y2s 2 and CG(y2) = 100 if y2> 2 for firm 2. Note that firm 2 faces a tighter capacity constraint. The market inverse demand function is p = 12 - y1-y2. The firms choose their production levels simultaneously and independently. a) Write down the profit functions of the two firms. b) Compute their best reply functions. c)Determine the Cournot-Nash equilibrium production levels.

Exercise 1 (MIT Sham School of Management) Consider the marked for bath inour- ance, Support Mat the market is comprised of f groups of prople of differing ry categories There we a dog and syed cooler of people in curb poop, bu inner manner bell whirl Suppose that the willingese to pay of prople in rach group is as Allows! Hisk 03 Actuarially fair premium Risk Premium a Complete the tells of artsandly fair insurance poonams that could be charged to mark compare is file willingness to part or. Will off the agents participate of this pricef / not what woolf is the composition of rule Facing the inearer? Woolf the premium found above be sufficient to cover the ride takes d Confiner with his logic. What will be the price of insurance in the squibbrim and which Solution. Actuarially fair premaimn Rick Premium 1200 a. The mixerindy fair porium is rapual to the expected kee = 10, tops risk. it is always breer than the willingness to pay sizes people exhibit risk mansion. h. I all agoris participate the chance of a kes in the population in a shake is SO. The1 The Nuh equalsrun is where the two praction functions intersect, which is where A = A = M. beach s coor the but mpong of the two imus we mutually corelstent, This is actually the only polit in which this is so, (Please clack this point by your own. Can you dial another Nash equilibrium?) This is the same in the competitive solution. Price is set sped to average (=marginal) out and one profits are make. 4. No beecave in lorecase In competition does not change the price set by the firms that canred be lower than meginalcat. This is the conne d the woo oilled Bertrand parade: Two Firms are enough to achieve the competitive outcome. Exercise 4 (Bertrand game with differentiated products) profits. The products or differentiated when common comder Men only inprat abdi hits Will a cerrone may be smiling fe buy the product of out producer, she will have When incentive to do this off the price of their farasrite product becomes too high To model has we allow the demand for rach good to deecod not only on the own price but aby an the price of the other paul Awwme for crumple that the demand for the good produced by Firml, go, and de demand where & is the arerage price that is fallen over the prices of the live forme. Nack Arm An arms food marginal cod c = 30. Supper the Frans can only choose between the Mirer J. Compair Me profits of the fris under the 9 different price combinations that are pasubir in the model 7. Using poo mover le Me precious point, refract Me Jel papi nairis for the sorad J. Find the (Bertrand Jack equilibrium of this pome. What are the profits at his ryguilt- Solution The polls of both fris will depend on lash prices and can be written in the blowing Substituting for the different Froms' price choices profits are chained and reported in the papel maris of the Bertrand pine with discret choion. I is way to show that both firms