The own price elasticity of demand for a pack of cigarettes is estimated to be -.4. Current price and consumption are $4.00 and 2 million units per year. Assuming a linear demand relationship determine the demand equation for cigarettes. Show all your calculations.

The production function for a firm is given by

Q = L+K+LK where Q denotes output; Land K labour and capital inputs. Wage rate and rental rate are given by w and r respectively.

(a) Show whether or not the above production function exhibits diminishing marginal productivity of labour.

(b) Determine the nature of the Return to Scale as exhibited by the above production function

(c) Using the Lagrangean Multiplier method, calculate the least cost combinations of labour and capital and the resulting long run total cost function for the above production function. Explain the economic significance of the Lagrangean Multiplier and calculate its value.

(d) Using Excel- Solver verify your answer to (d) above.