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1.You are given a specific supply function; Q = 20P, Where Q, is quantity supplied and P is price per unit in Kwacha a) Derive the producer's supply schedule b) Derive the producer's supply curve c) What things have been kept constant in the given supply function d) What is the minimum price that this producer must be offered in order to induce him to start supplying good X to the market? 11

2. Alfred Davis and his brother-in-law Hans Wilsdorf founded Wilsdorf and Davis, the company that would eventually become Rolex SA, in London, England in 1905. Wilsdorf and Davis' main commercial activity at the time involved importing Hermann Aegler's Swiss movements to England and placing them in high-quality watch cases made by Dennison and others. These early wristwatches were sold to jewellers, who then put their own names on the dial. The earliest watches from Wilsdorf and Davis were usually hallmarked "W&D" inside the caseback.In 1908 Wilsdorf registered the trademark "Rolex" and opened an office in La Chaux-de-Fonds, Switzerland. The company name "Rolex" was registered on 15 November 1915. In 1919 Wilsdorf left England due to wartime taxes levied on luxury imports as well as to export duties on the silver and gold used for the watch cases driving costs too high and moved the company to Geneva, Switzerland, where it was established as the Rolex Watch Company The first self-winding Rolex wristwatch was offered to the public in 1931 (so-called the "bubbleback" due to the large caseback), preceded to the market by Harwood which patented the design in 1923 and produced the first self-winding watch in 1928, powered by an internal mechanism that used the movement of the wearer's arm. This not only made watch- winding unnecessary, but kept the power from the mainspring more consistent resulting in more reliable time keeping. Its name was later changed to Montres Rolex, SA and finally Rolex, SA. Upon the death of his wife in 1944, Wilsdorf established the Hans Wilsdorf Foundation, a private trust, in which he left all of his Rolex shares, making sure that some of the company's income would go to charity. Wilsdorf died in 1960; since then, the trust has owned and run the company. As of 2010 Rolex watches continue to have a reputation as status symbols. Describe with examples the type of growth (horizontal, vertical, organic, diversified or merger and acquisition) that Rolex has gone through from 1905. (15 Marks) b. Discuss out of the four market structure perfect competition, monopolistic competition, oligopoly and monopoly which market structure does Rolex belong to. (15 Marks) Discuss Rolex's geographic spread around the world and why is it important to have good international trade among countries. (20 Marks) a. --END OF EXAMINATION-- Foundation Asia Pacific University of Technology and more.

3.Write out this consumer’s constrained expenditure minimization problem, indicating (i) the objective, (ii) the objective function, (iii) the choice variables, and (iv) the constraint (note this is not the same as writing down the Lagrangian).

b. Write down the Lagrangian for this consumer’s constrained expenditure minimization problem and solve for the first-order conditions.

c. Based on part b, solve for the Hicksian demands for this consumer as functions of prices and the targeted level of utility, x^h (px, py, ubar) and y^h (px, py, ubar).

d. Using your answers from part c, solve for the consumer’s expenditure function as a function of prices and targeted level of utility, E (px, py, ubar).

e. The Marshallian demands that arise from this consumer’s constrained utility maximization problem can be shown to be equal to x* (px, py, I) = I/(2px) and y* (px, py, I) = I/(2py). Show that the indirect utility function for this consumer is given by V (px, py, I) = 1/2(I^2/(pxpy)) , and also show that V (px, py, I) is increasing in I and decreasing in px.

f. In class we learned that the indirect utility function and expenditure function are inversely related: if the maximum utility a consumer can obtain with income I is given by ubar = V (px, py, I), then the minimized expenditures required to obtain utility level u¯ are equal to E (px, py, ubar) = I. Set V (px, py, I) = ubar and solve for I from the value function above to demonstrate that E (px, py, ubar) = I, where E (px, py, ubar) is the expenditure function you found in part d, to show that V and E are inversely related.