tute3 - ECON1003 Tutorial 3 1(a Determine the first...

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ECON1003 Tutorial 3 1(a) Determine the first derivative of the following: (i) y = 7x 4 , (ii) y = 1/x 2 , (iii) y = x 1/2 + 4x – 8 (b) A firm has the following total cost and total revenue function TC = 1/3Q 3 – 9Q 2 +200Q +5050, TR = Q(120 – 10Q) Deduce the equations for the following functions: (i) marginal cost, (ii) marginal revenue (iii) average cost (iv) average revenue. 2. Find the first, second and third derivatives of the following total cost function: TC = q 3 /5 – 8Q 2 +5Q/2 +180 3. The demand function for a monopolist is P = 90 – 3 Q . (a) Derive expressions for TR , MR and AR . Evaluate TR, MR and AR at Q = 15. Hence, describe, in words, the meaning of each function at Q = 15. (b) Show that the demand function, AR and price are identical. (c) Show that the slope of the MR function is twice that of the AR function. (d) Calculate the value of Q at which MR is zero. Calculate the value of AR and TR when MR is zero. Calculate the maximum number of units which a sensible monopolist should sell. (e) Graph TR , MR and AR on the same diagram. Confirm the answers to part (d) graphically 4. Consider the function q = f(P). (i) What is the shape of the function if f’(P) > 0 for P < P*
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Unformatted text preview: and f’(P) < 0 for P > P* and f”(P) < 0 for all P > 0? (ii) What if f’(P) > 0 and f”(P) > 0 for all P > 0. 5. The cost of manufacturing laboratory benches is given by the total cost function, The price charged to educational institutes and commercial outlets are governed by the respective demand functions, P = 480 – 6 Q P = 915 –8 Q (a) Write down the equation for the profit function for each outlet. (b) Calculate the price and number of benches for which profit is maximized and minimized. Calculate the maximum profit. (c) Show that MR = MC when profit is maximized, and minimized. How would you distinguish between the maximum and minimum profits? 6. (a) Derive a general expression for the price elasticity of demand for the function Describe verbally how demand changes in response to price changes for this function, Q, P > 0. (b) (i) Evaluate the point elasticity , ε d , at P = 15 and at P = 30 ECON1003 Tutorial 31...
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