# Equilibrium price and output for the industry, and the effect on the equilibrium of an imposition of an ad valorem tax, in relation to Cobb Douglas.

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Now as the items are perfect substitutes we can write the equation as f(x1, x2) = x1 + x2. Now this is Cobb-Douglas if the function has the form f(x1,x2) = Ax^a1 x^b2, and provides us the utility function (Varian, 2010) and the graph shown in fig 3. For the production formula it would be Q=AK^ αL^β (Renshaw, 2009)as you can see both formulas are remarkably similar, as they both steam from the original theorem. So if we set A=10 and α= β=0.5, we get Q=10K^0.5L^0.5 now if we fix capital to say 49, just for the short run, we get Q=10(49)^0.5L^0.5 which we can rearrange so that we get Q=70L^0.5. Now to find the average product of labour or APL we divide Q by L, Q/L. So using Q=70L^0.5 we get 70L^0.5/L= 70L^0.5 (Renshaw, 2009). Obviously this is all in the short term, but if we wish to find it with terms of market value we would time the equation by the price so say our good is p=100 we get, Q=P(10K^0.5L^0.5) so with ours we get Q=100(10K^0.5L^0.5)=1000K^0.5^0.5 giving us the firms total revenue in term of sale price and labour and capital the firm hires.

Equilibrium price and output for the industry, and the effect on the equilibrium of an imposition of an ad valorem tax, in relation to Cobb Douglas. A perfectly competitive industry, an industry that has no barriers to entry or exit and allows all parties the same technology and resources. This, a perfectly competitive industry, is a type of industry, each type of industry varies in competitiveness depending on in part on how many suppliers are seeking the demand of consumers and the ease with which new businesses can enter and exit a particular market in the long run, so obviously the more there is the more competitive a market or industry is and vice versa. As such with less competition it becomes more expensive. The spectrum of competition ranges from highly competitive markets where there are many sellers, these have little to no ability to affect the market price. To a Monopoly where a market or

Cited: Lockwood, B. (2001). Competition in Unit vs. Ad Valorem Taxes. Warwick. Mochrie, R. (2012, October). Intermediate Economics 1. Lecture 8 . Edinburgh. Ormerod, P. (2012). Perfect competition - the economics of competitive markets. Retrieved from Tutor2u: http://tutor2u.net/economics/content/topics/competition/competition.htm Renshaw, G. (2009). Maths for Economics. Oxford university press. Varian, H. (2010). Intermediate Economics. W W Norton.

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