Mathematical Proof for Profit Maximisation (MC = MR) for Cambridge/ CIE A Level Economics

There is a reason why profit is necessarily maximised at MC = MR. When MR > MC, the firm should continue producing more output. The logic is, at this stage of production, for every one unit of output produced, it adds more to TR than to TC. As such, a rational producer would want to produce and sell more because there is room for supernormal profits to be further increased

At MC = MR, it implies that for every one unit of output produced, TR increases at the same pace as TC. Profit has therefore been maximised. There is no more room for any further rise in abnormal profit

It will not produce where MC > MR. This is because, for every additional one unit of output produced, it adds more to TC than to TR. While there are still profits to be made, it will not be at the position where they are maximised

Mathematical Relationship Between APC and MPC

The Basic Mathematics of Costing for CIE/ Cambridge A-Level Economics

The Most Common Errors Found in Paper 3 (9708) of CIE A Level Economics (8pm tonight, Malaysian time)

Chapter 1: Basic Economic Ideas and Resource Allocation

1. Unable to clearly distinguish between productive efficiency and allocative efficiency. The former happens when a firm is producing at the lowest cost possible. This is achieved when MC = AC. The latter happens when a firm is producing output that is valued by the consumers. If this happens, P = MC or AR = MC or MB = MC
2. Not being aware that all points on the PPC are productively efficient. However, it is possible that there can be only one point on the PPC which is allocatively efficient. It is also possible that NONE of the combination of two goods along the PPC can be regarded as allocatively efficient (refer to North Korea that focuses only on producing guns and nuclear. NONE of these two is wanted)
3. Unaware that social efficiency, MSB = MSC can only be achieved once all negative/ positive externalities have been taken into account
4. If P > MC, then the firm should produce more output. By contrast, if P < MC, then efficiency can be improved if the firm produces less (Basically, ‘no one’ values the good as indicated by lower MB than MC)

Chapter 2: The Price System and the Micro Economy
Theory of Firms 

1. Unable to perform calculations involving the AFC, AVC, AC and MC
2. Unaware that MC is actually the gradient of TC curve while MR is the gradient of TR curve (Mathematically, MR = change in TR/ change in quantity. This is equivalent to gradient where m = change in y/ change in x. Ever wonder why MR = 0 when TR is maximised?)
3. Frequently mixed up between profit maximisation (MC = MR), revenue maximisation (MR = 0) and sales maximisation (AC = AR)
4. Unaware that in an imperfect market, the only way for the output to be increased is for the price to be lowered
5. Most are unable to answer questions pertaining to the interpretation of diagrams. One of the reasons I notice is that, candidates do not practice sufficiently and have adequate understanding of the nature of each type of cost and revenue curve
6. Weak when it comes to the calculation of returns to scale. Instead of calculating and comparing the percentage of change between input and costs, candidates compare the difference in input against the costs (The key here is PERCENTAGE)
7. Always forget the fact that PED = 1 when TR is maximised
8. Unaware that a firm can still continue operating despite making a loss. It will only cease production when it cannot cover its own TVC. This can be written as P < AVC or TR < TVC
9. Thought that only perfectly competitive firms produce homogenous goods. This is not true. Oligopoly firms can also produce identical goods. Consider water, gas and electricity firms. They are very big, few in number and yet produce almost similar goods
10. Forget one of the assumptions of price discrimination and that is MC must equal to MR in both markets
11. Forget that PED > 1 when price is increased and PED < 1 when price is decreased. This supports the analysis of the kinked demand curve. Firms shouldn’t attempt to alter prices as it will cause their TR to fall
12. The most striking feature for a perfectly competitive firm is homogenous products, for a monopolistic firm is differentiated products, for an oligopoly would be high interdependence and monopoly is unique products
13. A perfectly competitive firm is both productively and allocatively efficient only in the LR. In the short run, it is productively inefficient. However, generally/ theoretically, all imperfect market firms are thought to be both productively and allocatively inefficient in both short-run and long-run
14. Unaware that MC depends on VC and not FC. So, when there is a change in the FC, value of MC will remain unchanged    

Theory of Cardinal Utility

1. Forget the fact that utility can only be maximised when two conditions are met. First, all the allocated money income must be spent. Second, MU per dollar for all the goods must be the same (in reality, this is not necessarily)
2. Weak when it comes to questions involving the budget line. Candidates almost always unable to determine the direction of money income and the price of a good given that the budget line has shifted in the mentioned position
3. Income effect and substitution effect of a price change for both normal and inferior good

Chapter 3: Government Microeconomic Intervention

1. Not familiar with the concept of demand for labour. Do take note that D_L = MRP_L which can be broken down into MP_L x MR. This means demand for labour will increase if productivity increases, there is a higher price for the final product and also if there is a rise in the demand for the final product (refer to the formula while going through this three. It will make much more sense)
2. MRP_L = MP_L x MR. This is the universal formula to calculate marginal revenue product of labour. However, in the case of perfectly competitive labour market, MR can be replaced with P because of the assumption of homogenous goods. For a monopsonist labour market, one CANNOT replace MR with P
3. Unaware that MC_L = MRP_L means profit maximising quantity of labour. In theory, firms will use such an approach to determine the number of workers to be hired so that profits can be maximised. Do take note that labour is just like any other input. They contribute to both cost and revenue. Under theory of firms, MC = MR means quantity of output to be produced so that profits can be maximised
4. Not being aware that trade unions are more successful in bargaining for a higher wage in a monopsonist labour market than perfectly competitive (Easier to be seen and understood if you compare the diagrams for both situations)
5. Always make mistakes for questions involving transfer earnings and economic rent